Question

One leg of a 45-45-90 triangle is 7 square roots of 3 units. What is the length of the hypotenuse round to the nearest tenth.

A. 9.9 units
B. 10.0 units
C. 10.6 units
D. 12.7 units

Answer 1

The length of the hypotenuse in a 45-45-90 triangle with a leg length of 7√3 units is calculated using the Pythagorean theorem, resulting in a hypotenuse approximately 17.1 units long when rounded to the nearest tenth.

Step-by-step explanation:

To find the length of the hypotenuse in a 45-45-90 triangle when one leg is known, we can use the Pythagorean theorem, which in this case simplifies due to the nature of the angles. For a 45-45-90 triangle, the length of the hypotenuse is √2 times the length of each leg since the legs are congruent. Given that one leg is 7√3 units, we calculate the hypotenuse (c) as follows:

c = leg length × √2

c = (7√3) × √2

c = 7√6

To approximate, calculate the numerical value:

c ≈ 7 × 2.449 (as √6 ≈ 2.449)

c ≈ 17.143

Rounding to the nearest tenth gives us 17.1 units. Therefore, option B. 10.0 units is incorrect, and the correct length rounded to the nearest tenth is actually 17.1 units, which is not one of the options provided.